A small ball of mass m starts at a point A with speed `v_(0)`. and moves along a frictionless track AB as shown. The track BC has coefficient of friction `mu`. The ball comes to stop at Cafter travelling a distance L which is:

Options

A. `(2h)/(mu)+(v_(o)^(2))/(2mug)`
B. `(h)/(mu)+(v_(o)^(2))/(2mug)`
C. `(h)/(2mu)+(v_(o)^(2))/(mug)`
D. `(h)/(2mu)+(v_(o)^(2))/(2mug)`

Answer

B

Explanation

Initial speed at point `A, u=-v_(0)`
Speed at point `B,v=?`
`v^(2)-u^(2)=2gh`
`v^(2)=v_(0)^(2)+2gh`
Let ball travels distance .s. before coming to rest
`S=(v^(2))/(2mug)=(v_(0)^(2)+2gh)/(2mug)=(v_(0)^(2))/(2mug)+(2gh)/(2mug)+(2gh)/(2mug)=(h)/(mu)+(v_(0)^(2))/(2mug)`